This paper presents a distributed output regulation algorithm for the leader-follower heterogeneous multi-agent system with unknown leader dynamics. The unknown nonlinear dynamics of the leader agent are reconstructed based on a data-driven transformation that lifts the nonlinear dynamics to a linear space that approximates it. An adaptive distributed observer algorithm is designed to estimate the leader states and its linear model approximation for each follower agent, since it is considered that the leader communicates only to a subset of followers. To design the output synchronization protocol, a local state feedback control is developed for each agent. The proposed algorithm is validated through simulation studies.